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# Functional shock test per mil-std-810 - equivalent static load

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## Functional shock test per mil-std-810 - equivalent static load

(OP)
Does anyone have a rule of thumb or calculation for the static equivalent load due to a shock test? This isn't a drop test but a shock simulating abuse during the products life. For example 40g's at 6 ms.

I have always used the g load times the mass of the part and never had any problem but this methodolgy is being questioned and I have no text to reference.

thanks

### RE: Functional shock test per mil-std-810 - equivalent static load

Not sure if there is an equivalence.  That's why hypervelocity projectiles work the way they do.

### RE: Functional shock test per mil-std-810 - equivalent static load

(OP)
wow - I expected to get a few more responses on this thing. I'll add a little more info. that might help move it along.

Figure 516.5-10 of the specifcation gives details on a Ideal sawtooth pulse and includes a note which describes the formula: Vi = 0.5*T*P
where: Vi = velocity change
T = time
P = peak acceleration magnitude

What one finds by using this calculation is that the acceleration is basically cut in half.
So heres the rub: When I make some assumptions about crumple zones and velcity/acceleration a 75g shock seems consistent with a vehicle crashing at about 50 MPH. Using half that value seems a little on the low side. In addition I've always used g loading in calcualtions without ever having it brought into question and the analysis was generally reviewed by old timers a lot smarter than me.

Help!?

### RE: Functional shock test per mil-std-810 - equivalent static load

this thinking may be too academic and simplistic for your purposes, but ....

if you assume constant acceleration (deceleration) then the acceleration experienced in stopping from velocity V0 over a distance X is

V02 / (2 X)

in a car crash from 88 ft/sec the front end stops say in 1/2 ft (6 inches) so it senses a deceleration of...

88*88/2/.5 / 32 = 242 g's

the car crushes and the back end stops in 5 feet, so it senses...

88*88/2/5/32 = 24.2 g's.

this of course is a completely inelastic impact.... ignoring  elastic shock responses through the car during the event, but you asked for the overall static equivalent shock and the answer seems to be ... well it depends on where you are in the car...

regards

magicme

------------------------------------
there's no place like gnome.

### RE: Functional shock test per mil-std-810 - equivalent static load

i left out a sentence....

so the front end sees 242g's for .0114seconds and the back end sees 24.2 g's for .114 seconds  (using an average 44 fps velocity during the crash to calculate time)

magicme

------------------------------------
there's no place like gnome.

### RE: Functional shock test per mil-std-810 - equivalent static load

(OP)
Thanks for all the responses. The responses have all been helpful. What I'm hoping to find is someone that has used an anaylitical method for the MIL-STD-810 shock test similar to what is done for random vibration. For random vibration it is common practice to use the Miles equation, 3 sigma, Miners equation, etc to determine a conservative equivalent load and then design hardware to.
The MIL-STD gives a formula for the shock accleration but a couple of paticulars that concern me when trying to calculate stress are:
1. I think there are some issues relative to the rate of applied load (ie) strain RATE, with faster being worse.
2. I would think some safety margin would be used to account for the oops factor.

thanks

### RE: Functional shock test per mil-std-810 - equivalent static load

Maximum equivalent static deflection under shock can be determined from shock response spectra as follows:

d = A_eq * G / w_n^2

Were:
d = calculated equivalent static deflection in inches
A_eq = equivalent static acceleration in G’s
W_n = natural frequency of system in rad/sec

This equation applies strictly only to a single degree of freedom system, but is a good approximation for a dominant fundamental mode of vibration.

The equivalent static acceleration can be calculated using equations in Chapter 23 of the "Shock and Vibration Handbook", Third Edition.  See Equation (23.46) for half sine shock pulse.

These equations strictly apply only in the linear region of response.  If the material response is in the plastic region, then you have to account for the energy absorbed by the plastic deformation of the material.

Regards,
G Rudd

### RE: Functional shock test per mil-std-810 - equivalent static load

Take a pek at MIL-STF-810F, Method 514.5, para 1.3.1 - 1.3.3:

•    Acceleration loads are expressed in terms of LOAD FACTORS
o    For acceleration:  inertia load factors applied slowly enough and held steady for a period of time long enough such that the material has sufficient time to
•    fully distribute the resulting inertia loads, and
•    such that dynamic (resonant) response of the material is not excited.
•    Shock is
o    a rapid motion that excites dynamic (resonant) response of the material, but
o    with very little overall deflection (stress)
•    Acceleration vs Shock
o    Acceleration loads expressed in terms of load factors (g loads)
o    Shock environments also in terms of g loads, but
?    Acceleration (static) requirements cannot be satisfied by shock (dynamic)
?    Shock cannot be satisfied by acceleration
?    Acceleration test criteria and methods cannot be substituted for shock test criteria and methods.
Shock test criteria and test methods cannot be substituted for acceleration criteria and test methods

### RE: Functional shock test per mil-std-810 - equivalent static load

Take a peek at MIL-STD-810F, Method 514.5, para 1.3.1 - 1.3.3:

•    Acceleration loads are expressed in terms of LOAD FACTORS
o    For acceleration:  inertia load factors applied slowly enough and held steady for a period of time long enough such that the material has sufficient time to
•    fully distribute the resulting inertia loads, and
•    such that dynamic (resonant) response of the material is not excited.
•    Shock is
o    a rapid motion that excites dynamic (resonant) response of the material, but
o    with very little overall deflection (stress)
•    Acceleration vs Shock
o    Acceleration loads expressed in terms of load factors (g loads)
o    Shock environments also in terms of g loads, but
?    Acceleration (static) requirements cannot be satisfied by shock (dynamic)
?    Shock cannot be satisfied by acceleration
?    Acceleration test criteria and methods cannot be substituted for shock test criteria and methods.
Shock test criteria and test methods cannot be substituted for acceleration criteria and test methods

### RE: Functional shock test per mil-std-810 - equivalent static load

I have an old report on a shock analysis we did on a USN shipboard structure where we we used "shock design numbers" to simplify the analysis and turn it into a static problem.  My understanding is that if the pulse is 10msec or greater in duration then the shock design number method is a safe conservative approach.   The curves are in NRL Report 7396 (along with intelligent discussion, references, etc.).  I suggest you get that report.  All I have are the curves anymore.

Tunalover

### RE: Functional shock test per mil-std-810 - equivalent static load

yes, tunalover, you reminded me of this....

I think you are referring to NRL-1396 "Interim Design Values for Shock Design of Shipboard Equipment", May 1980.

that memo gives a series of equations and table for calculating shock "design loads" for equipment, based on it's fundamental frequency, mass, location on the ship, type of ship.

way back, I did plot up some graphs from the equations for quick use... the only one I can find, I posted here...

www.tikmark.com/NRL1396.jpg

at one time I also wrote a neat little calculator for doing these, but can't find it at the moment (it was several computers ago !! )

possibly this is useful

regards

------------------------------------
there's no place like gnome.

### RE: Functional shock test per mil-std-810 - equivalent static load

magicme-
I couldn't make sense of your attachment.  Maybe part of it was cropped off.  It's important to note that the G-level depends on the direction of application.  Athwartship is different from vertical is different from...Most certainly the vertical values will be greater than all other directions.

Tunalover

### RE: Functional shock test per mil-std-810 - equivalent static load

If we're going in to shipboard shock, there is a declassified 1968 document that is used for many of the FEA packages that offer DDAM (Dynamic Design Analysis Method).  DDAM uses an NRL method of sums to calculate accelerations and velocities based on natural frequencies and mass participation factors.  It then uses the lower value of the velocity based acceleration or the acceleration based acceleration.

Another reference to look at is NAVSEA-0901-LP-3010 (I think that's the full designation).

But all of these ship-related documents are based on some assumptions such as that this is a ship floating in water receiving a shock from a mine detonation on a steel ship.  The curves depend on whether this is a surface ship or submarine, equipment is hull mounted or deck mounted, which direction, etc.

I didn't get the impression that this situation involved ANY of this, and the development of these equivalent shock loads is inappropriate for anything other than ship-related shock.

### RE: Functional shock test per mil-std-810 - equivalent static load

The OP was describing drop and functional shocks, not 901D

### RE: Functional shock test per mil-std-810 - equivalent static load

tunalover .... yes, NRL-1396 has sets of data for each shock direction, mounting location, etc etc ... i only have that one screen capture graph that i could find at the moment.

GBor... i think this is the declassified document you refer to ... the original was dated 1963 and was revised in 1980 (maybe also later, but i don't know).  and you are correct .... this data applies strictly to shipboard equipment only.

and possibly all of this goes way beyond what the OP asked about ...?

regards,

magicme

------------------------------------
there's no place like gnome.

### RE: Functional shock test per mil-std-810 - equivalent static load

“40g's at 6 ms.

I have always used the g load times the mass of the part and never had any problem but this methodolgy is being questioned and I have no text to reference.”

Hmmm, the people who are asking must not know F=MA.  A is Gs (gravity) so bigger Gs times M is bigger force (Lbs).

Multiplying the Gs X Mass is correct to get the static load; however the time translates to the frequency that the 40g will be at full response.  The frequency would be 1/(2*.006) = 83 hz.  Anything that has a Fn of 83 hz will see 40g plus amplification.  With no damping (or 2% damping) and +/- 3 octaves from the Fn, your best case would be that a part will only see 40g.  It’s the part that has the same Fn as the shock input is the one you should be worried about.

Tobalcane
"If you avoid failure, you also avoid success."

### RE: Functional shock test per mil-std-810 - equivalent static load

To add, if you can get the time domain in a psudo velocity curve (SRS), you may figure out what the Gs are per freqeuncy.  So if you can figure out the frequency of the part, you can figure out what real Gs your part will see.

Tobalcane
"If you avoid failure, you also avoid success."

### RE: Functional shock test per mil-std-810 - equivalent static load

If you simply multiply the G load times the mass in order to try and determine the equivalent static load you are ignoring dynamics.  The shock amplification factor is a function of the ratio of the natural frequencies of the structure to the frequency of the shock pulse.  You need to multiply your G load times the amplification factor times your mass -> F= Amp_Factor*G_load*mass

Now for the tough part, how do you determine the amplification factor.  Well if you can approximate your system as a 1DOF, or 2DOF system, the response of these types of systems can be found in any text on vibrations.  In fact you can find them online.  There will be plots of amplification factor vs frequency ratio.  If you know the frequency ratio you can determine the amplification factor.  For instance, assume your structure has a fundamental frequency of 250 Hz and lets say the pule duration is .0085.  This translates into 60Hz.  Yor frequency ratio is 1.667.  From the response plot, the amplification factor is going to be (assuming 5% structural damping) ~1.55.  So if your shock input is 40 G's, you would actually multiply 62 G's by the mass of the structure.

However if you have closely spaced modes then there will be dynamic coupling and the amplification can be much, much higer.

If you have access to FEA software you can easily model these things.  Bottom line:  Unless the natural frequency is on the order of 10X higher than the frequency of the pulse, you need to have some amplification factor.

### RE: Functional shock test per mil-std-810 - equivalent static load

GBor

I stand corrected.
NRL7396 (that you refer to) is *not* the NRL1396 that I referred to.
They are separate documents.

regards,

magicme

------------------------------------
there's no place like gnome.

### RE: Functional shock test per mil-std-810 - equivalent static load

Thanks for checking that, magicme, I wasn't searching to see if you were wrong, but it's nice to be right every once in a while :)

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